CONJUGATE-GRADIENT METHODS FOR CONTINUATION PROBLEMS

We study linear and nonlinear conjugate gradient methods for large sparse continuation problems. First we show how the linear conjugate gradient methods can be incorporated as linear solvers in the context of efficient higher-order predictor-Newton corrector continuation methods. The implementation is based on the GMRES of Saad and Schultz. Next we describe how to use a special nonlinear conjugate gradient method to perform the corrector phase. In both cases we deal with the perturbed problems for the bifurcations. Sample numerical results concerning certain nonlinear eigenvalue problems are given.